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Trudy Mat. Inst. Steklov., 1984, Volume 165, Pages 143–170 (Mi tm2278)  

This article is cited in 18 scientific papers (total in 19 papers)

Local class field theory

A. N. Parshin


Full text: PDF file (3061 kB)

English version:
Proceedings of the Steklov Institute of Mathematics, 1985, 165, 157–185

Bibliographic databases:

Document Type: Article
UDC: 512.62

Citation: A. N. Parshin, “Local class field theory”, Algebraic geometry and its applications, Collection of articles, Trudy Mat. Inst. Steklov., 165, 1984, 143–170; Proc. Steklov Inst. Math., 165 (1985), 157–185

Citation in format AMSBIB
\Bibitem{Par84}
\by A.~N.~Parshin
\paper Local class field theory
\inbook Algebraic geometry and its applications
\bookinfo Collection of articles
\serial Trudy Mat. Inst. Steklov.
\yr 1984
\vol 165
\pages 143--170
\mathnet{http://mi.mathnet.ru/tm2278}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=752939}
\zmath{https://zbmath.org/?q=an:0579.12012|0535.12013}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1985
\vol 165
\pages 157--185


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. V. Vostokov, “Explicit construction of class field theory for a multidimensional local field”, Math. USSR-Izv., 26:2 (1986), 263–287  mathnet  crossref  mathscinet  zmath
    2. O. V. Mel'nikov, A. A. Sharomet, “The Galois group of a multidimensional local field of positive characteristic”, Math. USSR-Sb., 67:2 (1990), 595–610  mathnet  crossref  mathscinet  zmath  isi
    3. Fesenko I.B., “Multidimensional Local Theory of Class Fields”, Doklady Akademii Nauk Sssr, 318:1 (1991), 47–50  mathnet  isi
    4. S. V. Vostokov, G. K. Pak, “Norm series in multidimensional local fields”, J. Math. Sci. (N. Y.), 130:3 (2005), 4675–4688  mathnet  crossref  mathscinet  zmath
    5. S. V. Vostokov, F. Lorenz, “An explicit formula for the Hilbert symbol for Honda groups in a multidimensional local field”, Sb. Math., 194:2 (2003), 165–197  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. I. B. Zhukov, “On ramification theory in the imperfect residue field case”, Sb. Math., 194:12 (2003), 1747–1774  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. D. V. Osipov, “Central extensions and reciprocity laws on algebraic surfaces”, Sb. Math., 196:10 (2005), 1503–1527  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. A. G. Khovanskii, “An Analog of Determinant Related to Parshin–Kato Theory and Integer Polytopes”, Funct. Anal. Appl., 40:2 (2006), 126–133  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. M. A. Dubovitskaya, “On the Brauer Group of a Two-Dimensional Local Field”, Math. Notes, 81:6 (2007), 753–756  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. S. V. Vostokov, S. O. Gorchinskiy, A. B. Zheglov, Yu. G. Zarkhin, Yu. V. Nesterenko, D. O. Orlov, D. V. Osipov, V. L. Popov, A. G. Sergeev, I. R. Shafarevich, “Aleksei Nikolaevich Parshin (on his 70th birthday)”, Russian Math. Surveys, 68:1 (2013), 189–197  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. S. V. Vostokov, “Shafarevich's paper “A general reciprocity law””, Sb. Math., 204:6 (2013), 781–800  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. D. V. Osipov, “The unramified two-dimensional Langlands correspondence”, Izv. Math., 77:4 (2013), 714–741  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    13. D. V. Osipov, “Noncommutative reciprocity laws on algebraic surfaces: the case of tame ramification”, Sb. Math., 204:12 (2013), 1797–1810  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. S. O. Gorchinskiy, D. V. Osipov, “Explicit formula for the higher-dimensional Contou-Carrère symbol”, Russian Math. Surveys, 70:1 (2015), 171–173  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    15. S. O. Gorchinskiy, D. V. Osipov, “A higher-dimensional Contou-Carrère symbol: local theory”, Sb. Math., 206:9 (2015), 1191–1259  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. S. V. Vostokov, V. V. Volkov, “Explicit form of the Hilbert symbol on polynomial formal module for multidimensional local field. II”, J. Math. Sci. (N. Y.), 222:4 (2017), 394–403  mathnet  crossref  mathscinet
    17. Sergey O. Gorchinskiy, Denis V. Osipov, “Continuous homomorphisms between algebras of iterated Laurent series over a ring”, Proc. Steklov Inst. Math., 294 (2016), 47–66  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    18. S. O. Gorchinskiy, D. V. Osipov, “Higher-dimensional Contou-Carrère symbol and continuous automorphisms”, Funct. Anal. Appl., 50:4 (2016), 268–280  mathnet  crossref  crossref  mathscinet  isi  elib
    19. D. V. Osipov, “Adelic quotient group for algebraic surfaces”, St. Petersburg Math. J., 30 (2019), 111–122  mathnet  crossref  isi  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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